Examiner’s Report: A2 2006
B. Todd Huffman
164 students total sat the exam. A summary of the exam will appear at the end of this
report. The assessor remained in schools for one hour at the start of the exam. There
were two minor corrections announced during the exam; one in Part B question 8 and
one in Part B question 9. There is no indication that these corrections caused the
students undue difficulty. The specifics of these corrections will be mentioned in the
relevant explanations for those questions.
The mean for the entire exam was 54.823 marks with a standard deviation of 15.491
marks.
Part A Short Questions:
All of the short questions were to be attempted. Any questions left blank received a
zero mark.
Q1:
6 points total possible. Mean 4.963. Standard Deviation 1.243.
Meant to be a straightforward question that most students should have been able to
answer and it was.
Q2:
6 points total possible. Mean 3.854. Standard Deviation 1.487.
Maths question on eigenvectors and rotation of a matrix. The fact that the matrix had
a repeated eigenvalue threw a number of students off. The weaker ones did not
recognize an eigenvalue was repeated. Some that did recognize this fact then did not
find two orthogonal vectors to represent the basis of the repeated eigenvalue. A few
decided that a 2x2 matrix was sufficient for rotation given only two eigenvectors.
Nearly everyone knew how to build a rotation matrix given three eigenvectors.
Q3:
6 points total possible. Mean 2.799. Standard Deviation 1.797.
This question had three methods that could lead to a solution but the most popular
method used involved Gauss’s law. Nearly all students figured out that a cylinder or a
rectangular solid were the two best volumes over which to employ the law, but then
about half of them proceeded to integrate all the way from one plate to the other rather
than integrating from a place where the E-field would be zero to a place, still within
the dielectric, at a distance ‘x’ away. Most knew the boundary conditions at the
surface of at metal and the fact that the E-field could not penetrate that metal, but
incorrect calculations of the E-field left many confused as to how to obtain the surface
charge on the plates.
Q4:
6 points total possible. Mean 2.884. Standard Deviation 1.746.
It was expected that students would have little difficulty obtaining the wavelength of
light given the parameters of the problem. This was worth ½ the marks. The slit width
was included so that the single slit diffraction pattern would place a zero on top of the
second order peak from the grating. Consequently the first visible peak after the first
order was at the third order. This did trip up a number of weaker students as expected.
The high spread reflects the binary nature of the marks awarded for this problem.
Some students wasted time deriving the diffraction and single-slit diffraction formulae
and these derivations were not required.
Q5:
7 points total possible. Mean 3.329. Standard Deviation 2.355.
A very clever question involving a sphere with a permanent polarization charge, in
some ways an electric analog of a permanent magnet. There were many difficulties
with this problem and only the most astute managed to complete it for full marks.
Many could not recognize that, despite explicitly being stated in the problem, D had
to be zero everywhere as there were no free charges present.
Q6:
9 points total possible. Mean 4.604. Standard Deviation 3.023.
There was a great deal of confusion about resolving power and free spectral range.
Many students tried to combine these concepts and came up with etalons of only
about 10 atoms wide. There were two or three acceptable answers to this problem
depending on the specific criterion employed to determine the separation and whether
formulae were used for Resolving power, or derived from base principles. Many tried
to use the instrumental width and this was a bit tricky if you did not know exactly
what this concept implied. One of the biggest errors was to take the position of the
peak of one wavelength to land on the minimum of the other wavelength. Since this is
an etalon the minimum lands exactly in the centre between two peaks and this
criterion is far too strict.
Part B Long Questions:
Students were expected to do three of the 4 available long questions.
Q7:
131 students attempted. Mean 8.473. Standard Deviation 4.419.
A popular question that makes it absolutely clear that students need to be examined on
material which was within the first year syllabus as well as material in the second year
syllabus. A disturbing minority (~30%) could not properly employ Ampere’s law for
a long, thin solenoid. They often chose the wrong Amperian loop even though the
picture drawn was in the correct orientation. A figure of the solenoid should have
accompanied this question. Nearly all understood the meaning of Maxwell’s equation
which implies a changing magnetic field induces an electric field, but as expected
only ~30% realized that integrating this equation generates the same integral form as
Ampere’s law but with magnetic flux taking the place of current. Most of those who
could do this though then were able to find the correct loop over which to integrate
but a common mistake was to use the full radius of the core ‘a’ instead of an arbitrary
‘r’. Since very few had the correct expression for the electric field the next part about
the Poynting vector was very difficult. A non-trivial number of clever students (about
15 or so) actually then solved the general energy flux problem as a proof rather than
using their incorrect Electric field. This technique received full marks. Once this
section was done about ½ could obtain the correct expression for the energy in the
solenoid with the core ½ removed but often the extra factor of 2 disappeared without
explanation or comment.
Q8:
162 students attempted. Mean 13.4. Standard Deviation 5.243.
Clearly won the popularity contest. Mostly bookwork and many people received
perfect scores in this question. Some were comparing the frequency to the
conductivity rather than using the low-frequency limit approximation. Apparently, a
similar question appeared in a previous exam but involved communication to a
submarine with the transmitter out of water, requiring the air-ocean boundary to be
included in the calculation. This caused sufficient confusion that an explicit
announcement was made during the exam that both the transmitter and receiver could
be assumed to be under water. Many people obtained the correct depth but the most
common mistake was to use cycles per second instead of radians per second in the
calculation. Only one mark was lost for this oversight however.
Q9:
151 students attempted. Mean 10.39. Standard Deviation 3.624.
Only a few people even mentioned the properties of the light source required to
achieve Michelson circular fringes. This was not a large penalty however. After that
the middle parts of the question were pretty standard and nearly everyone did well
there. But there was great difficulty figuring out what the dual wavelength pattern
would look like. Quite a few wasted time trying to formally minimize the equation of
intensity without thinking about the obvious shape of what they had just written
down. Very few people could correctly explain what the interferogram of the
continuous, but narrow bandwidth, source would look like in contrast to the discrete
wavelength source. There was an almost universal aversion to sketching the two
interference patterns during the explanation. In quite a few cases I think this hurt the
students as their powers of descriptive eloquence were not up to the task. The
notation for ‘D’ changed ½ way through the question and this had to be explicitly
pointed out during the exam.
Q10:
44 students attempted. Mean 10.5. Standard Deviation 5.337.
Two classes of students did this unpopular question. The very good and the very
desperate. Hence the almost central mean but wide deviation. This was not a difficult
question but it is clear that many students employ an exam strategy that does not
include the study of polarization. Those that realized they could not attempt one of
questions 7, 8, or 9 would then turn to question 10 with little time left and did very
poorly. Those few who revised polarization realized that this was, in fact, not a
difficult question and often achieved high marks. Some did not pick up the hint in the
question rubric (“use ray diagrams”) that Maxwell’s boundary equation solutions
were not required but this did not seem to be a serious problem. Quite a number of
obviously clever students thought that, though a circularly polarized beam would split
into two beams through the crystal (correct), an unpolarized beam would generate a
continuous spread of light between the two extreme angles (incorrect)! Nearly
everyone knew that a high-powered laser incident on an absorbing Polaroid was a
singularly bad idea in terms of generating a polarized exit beam.
Summary of Exam
Speaking to students after the exam (who were achieving middle to low 2.1 work),
they indicated that the exam was difficult but fair. They were generally pleased with
the amount they managed to answer. Morale was fairly high.
However the mean for the exam was a full ten marks below the target of 65. I believe
this was due almost entirely to the length of the exam and not inherent difficulty. It
was clear that students were rushed at the end and could have obtained some large
fraction of those ten marks in many cases had have been more time.
Consequently, I would strongly recommend to next year’s examiners that they
carefully consider the short questions. In this case I think this exam would have
benefited by 2 additional easy short questions and all of the short questions requiring
one and only one result to be presented. In this case, and we are seeing this trend in all
the papers, every short question actually required at least two quantitative answers.
They are turning into mini-PartB questions, and I find this trend a concern.
This examiner believes the long questions were well set and were of about the right
length and difficulty. To me, question 7 points out an important principle, that second
year material builds upon the previous year; and therefore first year concepts are fair
game in a second year exam. Indeed I feel it important that some such material be
included in the context of an exam for which the student will be rewarded for good
work at the end of their career at Oxford. To only examine first year
Electromagnetism and optics in prelims that do not contribute to a final degree
classification strikes me as a bit unfair.